Simplify. Multiply and remove all perfect squares from inside the square roots. Assume $z$ is positive. $5\sqrt{14z^2}\cdot 4\sqrt{21z^3}=$
Let's start by multiplying the factors within and without the square roots: $\begin{aligned} 5\sqrt{14z^2}\cdot 4\sqrt{21z^3} &=5\cdot 4\cdot\sqrt{14z^2}\cdot\sqrt{21z^3} \\\\ &=20\sqrt{294z^5} \end{aligned}$ Now we remove all perfect squares from inside the square root: $\begin{aligned} 20\sqrt{294z^5}&=20\sqrt{7^2\cdot \left(z^2 \right)^2\cdot 6z} \\\\ &=20\sqrt{7^2}\cdot\sqrt{\left(z^2 \right)^2}\cdot\sqrt{6z} \\\\ &=20\cdot 7\cdot z^2\sqrt{6z} \\\\ &=140z^2\sqrt{6z} \end{aligned}$ In conclusion, $5\sqrt{14z^2}\cdot 4\sqrt{21z^3}=140z^2\sqrt{6z}$